There may be many unintended consequences of the race to prosecute Julian Assange, the WikiLeaks founder. But as he faces extradition to Sweden, where he is accused of rape, one of the more eccentric side effects has already become clear: the rise to prominence of the European arrest warrant.

This legal instrument has been controversial since it was introduced in 2003, creating everyday injustices; but rarely has anyone outside the small group of lawyers that handles cases really cared. Now followers of the WikiLeaks story wonder how Assange could be extradited with so few questions asked. Why, for example, can our prisons detain someone (Assange is currently on remand in Wandsworth prison) for an offence under Swedish law that does not exist in British law? And how can a judge agree to an extradition without having seen enough evidence to make out a prima facie case?

The 2003 Extradition Act originated in an EU decision agreed just one week after 9/11. It was sold to voters as a way of ensuring cross-border cohesion in prosecuting suspects wanted across Europe for terrorism and serious crime. The level of cohesion in criminal justice systems across Europe, the argument went, and their common obligations under the European convention on human rights, provided a sufficient basis of trust that an arrest warrant by an EU country could be agreed by the UK with little scrutiny.

It's been downhill from there. Around three people per day are now extradited from the UK, and there is little to suggest that the majority are terrorists or serious criminals. In fact those involved in the process agree that many of the cases are "trivial".

This month I watched proceedings in Westminster magistrates' court as Jacek Jaskolski, a disabled 58-year-old science teacher, fought an EAW issued against him by his native Poland. Jaskolski – also the primary carer for his disabled wife – has been in the UK since 2004. His crime? Ten years ago, when he still lived in Poland, Jaskolski went over his bank overdraft limit.

There are instances when unauthorised bank borrowing can have criminal elements, but this is not one of them. The bank recovered the money, and there is no allegation of dishonesty. A similar case in Britain would be a civil, not a criminal, matter.

But it is a criminal offence in Poland, where every criminal offence has to be investigated and prosecuted, no matter how trivial. As a result Poland requested 5,000 extraditions last year alone, accounting for 40% of all those dealt with by Britain. By contrast the UK made just 220 requests.

In 2008 a Polish man was extradited for theft of a dessert from a restaurant, using a European arrest warrant containing a list of the ingredients. People are being flown to Poland in specially chartered planes to answer charges that would not be thought worthy of an arrest in the UK, while we pick up the tab for police, court, experts' and lawyers' time to process a thousand cases a year. This whole costly system is based on the assumption that the criminal justice systems of countries such as Poland are reasonable enough that it is worth complying with all their requests.

The level of frustration with the failure of this assumption is now beyond question. Even David Blunkett, who as home secretary presided over the introduction of the system, has regrets. "There is room for improvement with the EAW," Blunkett told the Commons home affairs select committee this month. "When we agreed to the system we believed that people would act rationally." The government is now conducting a review into extradition, with a panel led by a former court of appeal judge and senior extradition barristers.

But the EAW is not a stand-alone measure – it was intended as part of a much more ambitious agenda for the harmonisation of criminal justice systems across the EU. In January the European evidence warrant is meant to come into effect. Like the EAW, this would require Britain to give automatic recognition to search warrants issued by member states.

By next December the UK is supposed to have adopted mutual recognition of other states' decisions on probation, bail, the transfer of prisoners, and the suspending of individuals' finances. The Lisbon treaty, should the UK opt in, would take things even further. Opting out would still mean implementing the measures already agreed, and prevent negotiation of measures being applied in the rest of Europe.

In both the Assange and the Jaskolski cases the EAW is set on a collision course where the labyrinthine world of EU mutual recognition meets the reality of defendants' rights. And suddenly the mutual confidence that the public are meant to have in the criminal justice systems of other EU states – in Sweden's immunity from pursuing a politically motivated rape claim, or Poland's ability to be reasonable – does not seem to exist after all.